Quiz 2: Quadratic Functions

Okay, I'm your scribe for today and as you might've already guessed, I'm Sandy. By the way Cherrie, great job on your scribe! As for myself, I hope I can do just as good. Except we didn't do that much in class today. We started with talking about today's homework which I'll get to later. We then went onto reviewing this weekends homework.

Today we seemed to be confused on how to fill in the table that was for homework. The first equation we did looked at was:
f(x) = x² + 5x + 6.

The first thing we would do with this is factor the equation..
f(x) = (x-2)(x-3)

Now that we've factored the equation, we're able to pin-point the roots/ y-intercepts/ zeros.
2, 3

**REMINDER: Don't forget to switch the signs (-, +)!
Negative (-) to positive (+) and vice versa.

Okay, so we have our roots and having the roots we can easily find the Axis of Symmetry.
Step 1: Add both roots together.
2 + 3 = 5
Step 2: Now that we have the sum of the two roots, we divide by 2 to find the center of the roots which is the Axis of Symmetry.
5 / 2

NOTE: It's a lot easier to work with fractions than decimals!

So the answer to what the Axis of Symmetry is:
x = 5 / 2

**REMINDER: Don't forget to put x = before the numbers!

Now that we've found the Axis of Symmetry (which is also the x-coordinate of the vertex) we're able to plug that number into the equation f(x) = (x-2)(x-3) to find the max or min value(which is also the y-coordinate of the vertex). This is how:

f(5/2) = (5/2 - 2)(5/2 - 3)

f(5/2) = (5/2 - 4/2)(5/2 - 6/2)

Lets stop right there just in case anyone doesn't understand how we went from - 2 to - 4/2 and from - 3 to - 6/2. Well going back to grade nine or so, we should know that when adding fractions the denominators have to be the same. And knowing that whatever we do with the bottom we must do to the top, we multiply the bottom (1) by 2 to be the same as 5/2 and then multiply the top (2) by 2 as well. The result is 4/2. We do the same for the - 3.

Continuing...

f(5/2) = (1/2)(-1/2)

f(5/2) = - 1/4

Your answer should look like this:

min y = - 1/4

And there you go, you've got your max or min value.

Okay! So lets recap.

- By factoring the equation we found the roots. 2, 3

- and with the roots we easily found the Axis of Symmetry. 5/2

- Knowing that the Axis of Symmetry is the x-coordinate of the vertex, we found half of the vertex. ( 5/2, ___)

- Plugging the Axis of Symmetry into the equation we found the max or min value which we also know is the same as the y-coordinate of the vertex. ( 5/2, -1/4 )

We're not finished yet, though. The easiest way to figure out if the parabola opens up or down is to look at the the sign (-, +) in front of the equation itself. Looking back at the original equation there was a + sign:

f(x) = x² - 5x + 6

The answer for whether this equation opens up or down is:

UP.

As for domain, everyone should know that. Like Mr. K says, "It's a gimme!"

With these particular parabolas, the domain with always be:

D: (- oo, oo)

The range (y-axis) is, just like the domain, smaller number, comma, then the larger number. This parabolas smallest number is the max or min value. If the number is a max value, the number goes where the "larger number" is placed -- after the comma. If the number is a min value, the number goes where the "smaller number" is placed -- before the comma. In this case, we have a min value so the range should look like this:

R: [-1/4, oo)

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The second thing thing we went over was question 2 on the worksheet. It looked like this:

Find the equation of the quadratic function given its vertex is (1, -2) and a point on the graph at (-2, 16).

The first thing we should do is find the easiest equation to put this information into. This happens to be this:

y = a(x-h)² + k

We know the vertex so we can easily put those numbers into the equation so it looks like this:

y = a(x-1)² - 2

We also know a point on the graph which are the x and y coordinates! Those fit into the equation as well like so:

16 = a(-2 -1)² - 2

Now all we have to do is solve for a!!

16 = a(-2 -1)² - 2

16 = a(-3)² - 2

16 = a(9) - 2

16 = 9a - 2

16 + 2 = 9a

18 = 9a

18/9 = 9a/9

2 = a

Now that you have a, you can now find the equation for the quadratic function.

y = 2(-2 -1)² - 2

Alright! I think i've covered everything and there you have it. With the simplest information you can find EVERYTHING you need. Great hey? (=

Today's homework is:

1.) Sign up for the websites that Mr. K posted up.

2.) Exercise 6!

Have fun guys!

ANNDD..

Last but not least, tomorrows scribe will be...

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melissa!!

Have fun! =)